MST@UNH A mathematics degree for

mathematics teachers

Karen GrahamUniversity of New Hampshirekaren.graham@unh.edu

http://www.math.unh.edu/~mathadm/mst/

Steve BensonEducation Development Centersbenson@edc.org

History and Overview of MST@UNH Began as an NSF-funded institute around 1960

Summer 3 = MST (residential summer program)

Designed to enable teachers to:• Deepen and broaden their mathematics background in core areas of geometry, algebra, and analysis;• Explore new content areas of mathematics;• Interact with faculty and students in small classes;• Share ideas and teaching approaches with teacher from different areas of the country and of the world;• Consider perspectives that allow them to help their own students learn mathematics more effectively.

Who are our students?

majority come from the Northeast US most of those from New England

nearly every state represented, including Hawaii and Alaska some international students every year

England, Canada, Turkey, Saudi Arabia, Nigeria, Brazil

Most are high school teachers

Prerequisite: equivalent of mathematics minor

Thirty credits approved by the Department of Mathematics 18 credits from the “core” sequence:

Higher Geometry for Teachers I & II Higher Algebra for Teachers I & II Higher Analysis for Teachers I & II;

Problem Solving Seminar (3 credits) Successful completion of a Concluding Experience (replaced comprehensive examinations)

• develop a mathematical portfolio*• successfully complete a comprehensive problem set in conjunction with a problem solving seminar

* Reference: Mary L. Crowley and Ken Dunn. The Mathematics Portfolio. American Mathematical Monthly, v. 102, n. 1, January 1995, pp. 19-22.

Degree requirements

Summer 1Session 1 (3.5 weeks) Session 2 (3.5 weeks)Geometry I Geometry II Mathematical Proof and Problem Solving

Summer 2Algebra I Algebra II + Elective(s) or +

Elective(s) Directed Reading during academic year, additional elective(s) during summer, or transfer credit

Summer 3Analysis I Analysis II

Problem Solving Seminar

Typical course schedule

Recent Electives:Number Theory Technology in TeachingTopology MathematicsDiscrete Mathematics Mathematics Education:*Probability and Statistics Software History of Mathematics AssessmentPythagoras and Cousins* Teaching StrategiesDissections and Area*Combinatorial Algebra*

*“topical” 1 credit modules

Future electives:Data MiningTheory of Equations1 credit history modules connected with core content area

Goals of the Concluding ExperienceProvide the opportunity for students to: demonstrate knowledge of the content and discourse of mathematics demonstrate the ability to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality. synthesize knowledge gained from the MST experience. make connections between and among the various mathematical experiences and between the MST coursework and the courses they teach. demonstrate/document mathematical growth and maturity. demonstrate what they can do with a piece of mathematics that they have not formally studied but are prepared to investigate. model a process of self-assessment and reflection.

Requirements of the Portfolio

A presentation, talk, workshop, or article that brings together several mathematical ideas (developed in consultation with and approved by faculty advisor). Responses to a set of questions pre-college students might ask. (responses must include a description of how the mathematics learned in the MST program could be used to answer the students' questions) A description of a mathematical insight participants have had during their MST program that has changed the way they think about mathematics as a discipline or the learning or teaching of mathematics, or made them think differently about themselves or their students as mathematics learners.

Requirements of the Portfolio (cont’d)

A review of 2 articles that the participants are asked to read over the period of their program - one in mathematics content at the level of the Monthly and one in mathematics teaching at the level of the Mathematics Teacher. The best test or assignment from each of the "core" courses, including a rationale for each choice A mathematical autobiography. An annotated list of courses taken

Problem Set/ Problem Solving SeminarProblem Set: 15 – 20 problems (of which 10 must be solved) 5 chosen from set of 5 pairs (connected by content area) Draft solutions reviewed throughout the summer Solutions must include proof that answers are correct Oral presentation/defense of problem set required

Problem Solving Seminar: Credit/No Credit Although taken in conjunction with the Problem Set, the Seminar is not based on the Problem Set (particulars problems from the Problem Set are not discussed Content includes general problem solving strategies, proof writing, plus additional content (e.g., AGM inequality, Number Theory, advanced core topics)

What brought you to MST?I applied to MST because I was interested in meeting more math teachers, and I was interested in doing something to help further my career as a teacher.

My wife has family in NH and MA so when I was looking for a program I checked those areas. When I found MST, I heard great things about it. I liked the fact that it’s not full of education classes that don’t make me a better teacher. … The math is challenging but I’m in classes with other teachers, not research mathematicians. My classmates and I have a better personal connection because of our teaching and math backgrounds.

I wanted to pursue a master’s degree but would have been unable to carry the course work during the year and work as well. This provided the perfect solution.

The focus on math and the summer only schedule was very appealing.

How do you feel about the MST program’s focus on mathematics?

Loved that! Too many teachers are getting masters degrees in generic “education” courses that I don’t feel to be particularly helpful.

I like that fact. I was surprised. I thought it was going to be more teaching how to teach mathematics as opposed to straight mathematics. I like the idea of having a Masters in mathematics.

At first, I wasn’t sure if MST was going to be the right program for me, because of the focus on mathematics. Over the summers spent at UNH, I found that I am really glad I chose a program with a focus on math. … (T)his program has positively influenced my teaching (and) I truly understand math more than I did before MST. I feel an incredible sense of accomplishment after going through this program.

Would you recommend MST to your friends and colleagues?

I would recommend this program without reservations. I would be very upfront about the stress induced by moving through material at such a rapid pace, but it was well worth it. The friends that were made in this program will be so for the rest of my life.

I have already recommended MST to friends and colleagues that are serious about building a solid mathematics foundation. I caution those that are only interested in earning a higher degree for a salary increase. MST is NOT for them.

Final student thoughts

MST has given me a rich introduction to higher mathematics.(I know there is still so much more to learn!)

Though the program brought challenges I never dreamed of experiencing, both intellectually and emotionally, … I am proud to say I am a graduate of the MST program.

I love that the program doesn’t seem to sacrifice high expectations just because we meet for a condensed period of time.

It was nice to walk down the halls and check with others after working 4 hours on my own.